# Editorial of the Golden Fall 2023 issue 48, Vol 15 No 4

William Baker, Issue 48 Editor, Vol 15(4) MTRJ

Hostos Community College, CUNY, Bronx, NY

Editorial by William Baker

This issue contains teaching research articles from a variety of countries in the global community of mathematics teacher-researchers investigating student learning and reasoning with math concepts, at a wide range of educational levels. At the elementary level, it includes a teaching research article on children struggling to learn fractions in the Philippines, at higher levels of secondary education it includes teaching-research into the difficulty students have with trigonometry in Nepal, as well as the benefits and drawbacks of calculator usage in Vietnam.

At the undergraduate level, this issue includes teaching research on the difficulties student have in proving the irrationality of certain radical numbers in Afghanistan, and from Vietnam there is an article on the pedagogical technique referred to as the flipped classroom combined with the software GeoGebra to promote problem solving, also from Vietnam is a paper on the construction of a rubric for the analysis of medical student’s use for statistical reasoning. An article from Columbia represents an excellent example of teaching-research that employs a cyclical approach to improving mathematical pedagogy through design-strategy, classroom implementation, followed by quantitative-qualitative assessment alongside the design of artifacts for undergraduate instruction by integration of mathematical modeling into STEM education. A teaching-research article on the use of optimization within the instruction of undergraduate Engineering students from Malaysia demonstrates the pedagogical importance of modeling real-life problem-solving situation in that field.

Alongside these teaching-research articles this issue also contains two articles focused on teacher development, the first investigates to what extent pre-service teachers in Turkey can assimilate constructivist pedagogy focused on the Realistic Mathematics Educational approach (RME). The second, examines the exposure and attitude existing secondary education teachers in the Philippines have towards educational research.

**Content**

**The Use of Calculators in Teaching Mathematics: A Survey in Vietnam**

*Nam Danh Nguyen and Hung Van Nguyen (Vietnam) p.5*

This teaching research article is an investigation into the effects of the use of calculators in the educational system in Vietnam. The view of educators and teachers in Vietnam is that the use of technology has a positive effect on student affect through encouraging discovery and more conceptual approaches to problem solving yet, many educators are concerned with a possible decline in computational skills that may hinder mathematical thinking, and thus have a negative view of the use of calculators. The authors note that access to graphing calculators is very uneven in Vietnam and that teaching material to implement such technology is lacking. These authors’ research into their own teaching with calculators supports both such positive aspects as well as reduced emphasis on basic computational skills. They conclude that professional development with an emphasis on how to effectively use calculators is critical for promoting conceptual learning within the problem-solving process is needed in Vietnam.

**An Analysis of Realistic Mathematics Education Activities of Pre-service Teachers Trained with a Constructivist Approach**

*Emel Çilingir Altıner, Halil Önal, Alper Yorulmaz (Turkey) p.26*

This article represents research to analyze preservice teachers’ proficiency with a Constructivist foundation referred to as Realistic Mathematics Education RME, in Turkey. In this study of 137 preservice primary education teachers, the authors note that these teacher candidates, although educated in RME, a constructivist-based methodology, often struggled to overcome more traditional patterns of instruction. They conclude that a change from an approach to math education where every answer is either right or wrong based upon a calculation to one of discovery and construction of meaning would require system wide implementation beginning at the undergraduate level. The authors suggested that more professional development and training, a system wide mentorship program and a platform for teachers to share their resources, ideas, and experiences with each other would support such efforts.

**Building framework for assessing students’ statistical reasoning in solving real-life medical problems**

*Hien Tran Thuy, Son Le Phuoc (Vietnam) p.45*

This study looks at the statistical learning and reasoning needed for the medical professions. This is clearly an important area of research given the increasing need for strong statistical understandings in the medical fields. In this paper the authors construct a framework to analyze medical student’s statistical reasoning based upon Bloom’s taxonomy, and PISA mathematics literacy classification. This framework was then used to assess student competency in solving real-life problems in the medical field.

**Combining flipped classroom and GeoGebra software in teaching mathematics to develop math problem-solving abilities for secondary school students in Vietnam**

An Thi Tan Nguyen, Hung Nguyen Thanh, Cuong Le Minh, Duong Huu Tong, Bui *Phuong Uyen, Nguyen Duc Khiem (Vietnam) p.69*

This teaching-research study examines the effect of using a flipped classroom teaching model with the software GeoGebra on learning outcomes, and student problem-solving. The authors employ an experimental-control group methodology with statistical analysis on pre and post test results.

**Assessing the Implemented Research Lesson Using Mathematical Quality of Instruction**

*Zyrine Joy Morillo, Kim Gabrielle Del Puerto, Joyce Ann Alag, Julius Christopher Doolittle, and Minie Rose C. Lapinid (Philippines) p.98*

This teaching research article focuses on fractions, a difficult foundational concept in elementary education. These authors review and analyze teachers’ craft proficiency and content knowledge using the Mathematical Quality of Instruction Rubric. The authors make practical suggestions for improvement of fraction pedagogy including: the ability to communicate with students and explain content knowledge, making good connections between the different fraction representations, exposure to pattern generalization to prepare for algebra, and the importance of teaching and modeling explanations that go beyond short one-, or two-word responses.

**Problematic and Supportive Aspects of Indirect Proof in Afghan Undergraduate Students’ Proofs of the Irrationality of √3 and √(5/8)**

*Ahmad Khalid Mowahed, Jawed Ahmad Mayar, (Afghanistan) p.124*

In this teaching research article, the authors investigate the difficulties and challenges their undergraduate student faced in reasoning about and specifically proving the irrationality of different radicals through extending or generalizing the proof of the irrationality of radical two. The authors identified the difficulties student had making appropriate connections necessary to generalize the proof of irrationality of two to composite numbers as well as radicals of rational numbers, they also proposed and explored alternates methods for proving irrationality.

**Mathematical Modelling, Integrated STEM Education and Quality of Education for Linear Algebra and Vector Calculus Courses**

*Sandra Barragán, Orlando Aya, Camilo Soto (Columbia) p.136*

This teaching-research article concerned an integrated approach to STEM education through mathematical modelling conceived of from a variety of vantage points, to improve student performance in advanced undergraduate classes of Linear Algebra and Vector Calculus in Columbia. This research was conducted in a cycling manner involving strategy-design, classroom-implementation, and then quantitative assessment, and produced classroom material as artifacts.

**Bridging the Gap Between Theory and Practice: The Research Productivity and Utilization of Research Outcomes Among Secondary Mathematics Teachers**

*Roldan S. Cardona (Philippines) p.164*

This article investigates what 211 High School mathematical teachers in Philippines think about research on teaching, in particular, whether it can enhance their experience with professional development. The methodology is through qualitative interviews, and the authors conclude that while High School teachers have very limited exposure to research, yet within a supportive environment they are willing to participate and recognize the importance of research for their teaching craft.

**Students’ Experience in Learning Trigonometry in High School Mathematics: A Phenomenological Study**

*Sandip Dhungana, Binod Prasad Pant, and Niroj Dahal (Nepal) p.184*

The teaching research paper is motivated by teachers’ difficulty in explaining trigonometry and students’ difficulty in understanding trigonometry in Nepal. This paper borders on action research in that it relies heavily upon the teacher-researcher’s personal experience in the classroom, as such it is qualitative research designed to improve the educational experience, specifically, to promote higher order thinking in the math classroom.

**Teaching the Mathematical Optimization Concept to First-year Engineering Students Using a Practical Problem**

*Hosseinali Gholami, Nur Azam Abdullah, Adib Hamdani (Malaysia) p.202*

This teaching-research article aims to establish a relationship between Calculus real-life optimization problems, and suitable and practical problem-solving for engineering students, as opposed to studying mathematics in an abstract vacuum. Data was gathered through surveys and subsequently analyzed using frequency analysis. This article incorporates feedback and insights from both students and professors obtained during the research, and should be of interest to educators, especially those of Calculus and civil engineering students.

**The Problem Corner**

*Ivan Retamoso, Editor (USA) p.222*

The police officer and driver problem, proposed I. Retamoso, solved A. Kumari

The looking for a pattern problem, proposed C. Ingrassia, solved A.Kumari.

Two new problems, one by I. Retamoso, and another by M. Ecker.